Tuesday, February 17, 2009

So beyond indeed, is the static realization of the structure of things. This is a more definable recognition of something that is very fluid and expressive. It is by our own humanistic natures that we like to compartmentalize?

"There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning." Albert Einstein (1879- 1955)

While this quote of Einstein is somewhat revealing of what can flash across the mind, it is by intense work that such a time allows for things to gather, and in this work, it will inevitable makes sense. Such cultivation allows for new things to be born and in such nurture and contemplation, something will eventually emerge.

A picture of flux lines in QED (left) and QCD (right).

Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!

This points to a reductionistic view about the nature of reality. That we are part and parcel creating the constituents of the reality that we see, has a glue that binds, and keeps it together. For each this glue is a process that has meaning for each of us. While one would wonder where such motivation would allow each to perceive it as so one might ask what value is assign each stage of expression to see that such a scale has been reduce to a quality of a kind? It's music?

Cover of Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond by Lawrence M. KraussViking Press

Guide Review - Hiding in the Mirror by Lawrence KraussIn Hiding in the Mirror, astrophysicist and cosmologist Lawrence M. Krauss addresses the concept of extra dimensions, from its appearance in popular culture such as Alice in Wonderland and The Time Machine to theoretical physics areas such as the theory of relativity and string theory. In fact, I would say that the book splits roughly 50/50 between cultural and scientific topics, which is part of the point of the book (that extra dimensions are tied to both areas), but for those who are specifically interested in the scientific aspects there are other books (such as Lisa Randall's Warped Passages) which address the scientific aspects in far more depth.

According to Krauss, extra dimensions have captured the human imagination well before it entered into exploration by physics in the last century or so. The book covers how the concepts were viewed by those in the past, as well as more recent science fiction, such as Star Trek (one of Krauss' favorite topics, as author of the bestselling The Physics of Star Trek). Much of this material is entertaining, but for those who are wanting to get to the heart of the physics, it can feel like filler.

About 100 pages of the book focuses on the recent work to find a unified theory of quantum gravity, focusing predominantly on string theory (with some mention of predecessors). This has been one of the areas where extra dimensions have become extremely dominant. Though Krauss exhibits some genuine skepticism about the track string theory is on, I think calling the book a criticism of string theory would be going a bit far. Krauss is placing string theory within a larger framework of extra dimensional movements in the past, many of which have proved incredibly enlightening and some of which have not done much. It's left to other books to determine whether string theory has any scientific merit.

This is part of the education of my learning to understand the implications of the work of Riemann in context of the Riemann Hypothesis. Part of understanding what this application can do in terms helping us to see what has developed "from abstractions of mathematics," to have us now engaged in the "real world" of computation.

I look forward to the help in terms of learning to understand this "ability of the mind" to envision the dynamical nature of the abstract. To help us develop, "the models of physics" in our thinking. To learn, about what is natural in our world, and the "mathematical patterns" that lie underneath them.

What use the mind's attempt to see mathematics in such models?

"Brane world thinking" that has a basis in Ramanujan modular forms, as a depiction of those brane surface workings? That such a diversion would "force the mind" into other "abstract realms" to ask, "what curvatures could do" in terms of a "negative expressive" state in that abstract world.

Are our minds forced to cope with the "quantum dynamical world of cosmology" while we think about what was plain in Einstein's world of GR, while we witness the large scale "curvature parameters" being demonstrated for us, on such gravitational look to the cosmological scale.

So while we have learnt from Ulam's Spiral, that the discussion could lead too a greater comprehension. It is by dialogue, that one can move forward, and that lack of direction seems to hold one's world to limits, not seen and known beyond what's it like apart from the safe and security of home.

It seems only the good scientist John Baez had epitomes the construction of the Platonic solids? A revision then, of the "time line of history" and the correction he himself had to make? Let's not be to arrogant to know that once we understand more and look at "the anomalies" it forces us to revise our assessments.

The Art form

I relayed this image and quote below on Clifford's site to encourage the thinking of young people into an art form that is truly amazing to me. Yes I get excited about it after having learnt of Gauss and Reimann's exceptional abilities to move into the non euclidean world.

Some think me a crackpot here? If you did not follow the history then how would you know to also include the "physics of approach," as well? Also, some might ask what use "this ability to see the visual abstraction" and I think this art form is in a way destined, to what was kept in glass cabinets and such, even while the glass cabinet in analogy is held in the brain/space of them) who have developed such artistic abilities.

It's as if you move past the layers of the evolution of the human being(brain casings) and it evolution and the field that surrounds them. Having accomplished the intellect( your equations and such), has now moved into the world of imagery. Closet to this is the emotive field which circumvents our perspective on the greater potential of the world in the amazing thought forms of imagery. This move outward, varies for each of us from time to time. Some who are focused in which ever area can move beyond them. This paragraph just written is what would be considered crackpot(I dislike that word)because of the long years of research I had gone through to arrive at this point.

Of course, those views above are different.

Mapping

Is it illusionary or delusional, and having looked at the Clebsch's Diagonal Surface below, how is it that "abstraction" written?

There is no doubt that the long road to understanding science is the prerequisite to mapping the images from an equation's signs and symbols. While not sitting in the classroom of the teachers it was necessary to try and move into the fifth dimensional referencing of our computer screen to see what is being extolled here not just in image development, but of what the physics is doing in relation.

So of course to be the historical journey was established like most things, Mandelstam current and what is happening there as an interlude, as well as helping to establish some understanding of the abstractions that had been developed.

But yes, before moving to current day imagery and abstraction, I had to understand how these developments were being tackled in today's theoretical sciences.

Wednesday, April 12, 2006

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?

My first demonstration was with a Calabi Yau model of the torso. Visually seeing this way, helped to progress understanding. The transferance from the math structure to imaging in computer, to me, seemed very hard thing to do.

How such reductionism is held to the values of science, is seen in the work of the calorimeters. Glast and LHC designs give introspective views of how fine our perspective is being shaped. Can we see the underlying imaging as a toll, respective of reductionism as seeing the dynamical and geoemtrical background to all events measured? LIGO in data accumulation, describing the infomration released into the bulk perspective.

For the roads leading to one's view of the strange world of non-euclidean views had to offer, I of course needed some model from which to work. As I looked at the model above and the transfer of higher dimensional thinking, the very idea and contrast to the lower image represented, how would you associate gravity in the diagram but watch the circle valution along side of gravity that emegres from the 2d discription as a energy valution, and relationship to gravity, evolving from mass, energy interconnectivity. I have to apologize as I was developing and am developing.

I do not know if this is right to assign my view above, while one did not know the evaluation of 1R as I watch DRL assessment of what can no longer be considered as valid, I have to wonder why such observations are not thought about more intricately as the valuation of that circle is considered. The comparison was drawn between the two pictures of the spacetime fabric above here, and below.

So if you follow the dimensional analysis, there is a systemic procedure that one has to follow, that does not have to be held in context of KK interpretation to this point, but it does help if you think about the very basis of this graduation that certain statements make themself known.

Would you dimiss a comment by Greene because of the speculation you have felt about him that you might not recognize, what is being said as you watch that circle develope alongside of the sphere, as it moves through the 2d discription? Here's what mean, as I had focused on Brian Greene's words.

The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

Of course I am cocnerned about the determinations of the paticle natures seen in a particular light. These constituent s are part an dparcel of a much larger view from increase entrophy( I always get these things a**backwards), and cooling temperatures?

Of course I am paying attention and listening. :)Of course I want to find my way back to the classical world from where probabilistic valuations reigned. I was acting as a "gathering point" in my quest for a "philosophical design" (not to be confused with ID?). :) Okay, I understand this is not acceptable.

What motivated such cosmlogical design, as a crunching inevitable to have found the limitations of the energy having found itself turning back? So we do not see this right now and we speculate. this did ont take away from the isolated examples of unfoldment as a cyclcical process between energy and matter did it??

Those are strong words [shut up and calculate] for a layman to consider, when he is groping to trying to find his way.

Lecture 23 was pointed out by Lubos Motl in his article for consideration. More was considered from the list contained here.

If such energies were to be amongst the recognition of the quantum world, had we really been that separated from cosmological recognition of what constitued that beginning? Am I suppose to dismiss Weinberg in his first three minutes, for what might have been recognized in the first three seconds?? Remeber I am in the fifth dimension, where temeprature and entropic findings would have found a furthe rvalue to the discussion of what went this way and what that way. The entangling process is very profound.

So in looking back, we do not know where such a thing could begin? I think I understand that from what , although, if such proceses were recognized in the cyclcial nature of the cosmos why would we not entertain the rejuvenation of geometrical propensities to models inherent already in the universe? See the universe as a much "larger process" much different then the scope through which we might have treated each galaxy in it's rotations? Everett? Hmmm....

I have been troubled indeed by the "orbital mapping" I speculated to the cosmological design, seen as "events" in that cosmo. By such happen stance, such relations seem to spark some wonder about the arrangement, to the fundamental library of that same orbital design. I made this mistake before, and I need to correct it now.

The collider ring as a boson, whose overall contention could have been seen in the total energy involved, and the dispensing to those extra dimensional perspectives within the "natural world" of our settings? Have I misunderstood the values of the Pierre Auger experiment to see better, then we had seen before, not to have seen a topological question about how one would interpret the sphere with one hole, as a donut? What values circles then?

Angels/demons seem to make there way into view here? Yet in the world of Dirac might he seen the consequence of possible pathways in the construction of the matrix involved and intoduced the i of questionable directives as results in the arrangement of that same matrix?? Feynman took over for sure in his toy models.

Then of course I come across this statement previous and I am back to scratching my head. Oh boy!

Saturday, October 01, 2005

How far indeed the the imagination can be taken to see such processes enveloped in how we percieve these changes all around us. Why is gravity so weak, here and now. I have jumped ahead but will lead into it from the other end of this article.

Never before had I encountered the reasoning of imaging behind the work of "conceptual frameworks" now in evidence. In how a mathmatician, or a scientist, like Einstein or Dirac, had some basis at which the design, of all that we endure, would have its's counterpart in this reality as substantial recognition of what must be done.

I don't think anyone now in the scientific arena needs to be reminded about what it takes to bring theory into the framework of cultural and societal developement, to see how it all actually is working. On and on now, I see this reverberating from Lisa Randall to all scientists that we encounter from one blog to the next, a recognition and developement of this visualization ability.

That Famous Equation and You , By BRIAN GREENE Op-Ed Contributor in New York Times, Published: September 30, 2005

There are two links here.One by Peter Woit with reference to article and one toSean Carroll who further illucidates the article by Brian Greene.

So here I am at the other end of this referenced article, that other thoughts make their way into my mind. Previous discussison ongoing and halted. To todays references continued from all that we had encountered in what General Relativity surmizes.

That this issue about gravity is very real. So that's our journey then, is to understand how we would percieve the strength and weakness through out the spacetime and unification of a 3 dimension space and one of time, to some tangible reality within this coordinated frame Euclidean defined.

So indeed I began to see this space as very much alive with energy that had be extended from it's original design to events that pass through all of creation, then how indeed could two views be established in our thiniking, to have Greene explain to us, that the world holds a much more percpetable view about what is not so understood in reality.

All the while the ideas that would leave gravity without explanation in a flat euclidean space, gravity would have been left to that solid response without further expalnatin in a weak field manifestation. But it was always much more then this I think.

While being caution once on what the quantum harmonic oscillator is not, Smolin did not remove my thinking of what was all pervasive from what this "empty space" might have implied, that heretofor "it's strength" was a measure then of a bulk, and what better way in which to see this measure?

Taken in context of this succession, this place where such conceptual framework had been taken too, it was very difficult not to encounter new ways in which to understand how gravity could changed our perceptions.

Thalean views were much more then just issues about water and all her dynamical explanations. It presented a new world in which to percieve dynamical issues about which, straight line thinking could no longer endure. A new image of earth in all it's wander, no less then Greene's analysis to how this famous equation becomes evident in our everyday world. It presented a case for new geometries to emerge. Viable and strengthened resolve to work in abstract spaces that before were never the vsion of men and women who left earth. Yet it all had it's place to endure in this succession that we now have adbvanced our culture in ways that one would not have thought possible from just scientific leanings.

Tuesday, July 26, 2005

Cassini Plasma Spectrometer (CAPS) The Cassini Plasma Spectrometer (CAPS) is a direct sensing instrument that measures the energy and electrical charge of particles such as electrons and protons that the instrument encounters. CAPS will measure the molecules originating from Saturn's ionosphere and also determine the configuration of Saturn's magnetic field. CAPS will also investigate plasma in these areas as well as the solar wind within Saturn's magnetosphere.[1]

Cosmic Dust Analyzer (CDA)

The Cosmic Dust Analyzer (CDA) is a direct sensing instrument that measures the size, speed, and direction of tiny dust grains near Saturn. Some of these particles are orbiting Saturn, while others may come from other solar systems. The Cosmic Dust Analyzer onboard the Cassini orbiter is ultimately designed to help discover more about these mysterious particles, and significantly add to the knowledge of the materials in other celestial bodies and potentially more about the origins of the universe.[2]

Composite Infrared Spectrometer (CIRS)

The Composite Infrared Spectrometer (CIRS) is a remote sensing instrument that measures the infrared light coming from an object (such as an atmosphere or moon surface) to learn more about its temperature and what it's made of. Throughout the Cassini-Huygens mission, CIRS will measure infrared emissions from atmospheres, rings and surfaces in the vast Saturn system to determine their composition, temperatures and thermal properties. It will map the atmosphere of Saturn in three dimensions to determine temperature and pressure profiles with altitude, gas composition, and the distribution of aerosols and clouds. This instrument will also measure thermal characteristics and the composition of satellite surfaces and rings.[3]

Ion and Neutral Mass Spectrometer (INMS)

The Ion and Neutral Mass Spectrometer (INMS) is a direct sensing instrument that analyzes charged particles (like protons and heavier ions) and neutral particles (like atoms) near Titan and Saturn to learn more about their atmospheres. INMS is intended also to measure the positive ion and neutral environments of Saturn's icy satellites and rings.[4]

Imaging Science Subsystem (ISS)

The Imaging Science Subsystem (ISS) is a remote sensing instrument that captures images in visible light, and some in infrared and ultraviolet light. The ISS has a camera that can take a broad, wide-angle picture and a camera that can record small areas in fine detail. Scientists anticipate that Cassini scientists will be able to use ISS to return hundreds of thousands of images of Saturn and its rings and moons. ISS includes two cameras; a Wide Angle Camera (WAC) and a Narrow Angle Camera (NAC). Each uses a sensitive charge-coupled device (CCD) as its detector. Each CCD consists of a 1,024 square array of pixels, 12 μm on a side. The camera's system allows for many data collection modes, including on-chip data compression. Both cameras are fitted with spectral filters that rotate on a wheel—to view different bands within the electromagnetic spectrum ranging from 0.2 to 1.1 μm.[5]

Dual Technique Magnetometer (MAG)

The Dual Technique Magnetometer (MAG) is a direct sensing instrument that measures the strength and direction of the magnetic field around Saturn. The magnetic fields are generated partly by the intensely hot molten core at Saturn's center. Measuring the magnetic field is one of the ways to probe the core, even though it is far too hot and deep to actually visit. MAG's goals are to develop a three-dimensional model of Saturn's magnetosphere, as well as determine the magnetic state of Titan and its atmosphere, and the icy satellites and their role in the magnetosphere of Saturn.[6]

Magnetospheric Imaging Instrument (MIMI)

The Magnetospheric Imaging Instrument (MIMI) is both a direct and remote sensing instrument that produces images and other data about the particles trapped in Saturn's huge magnetic field, or magnetosphere. This information will be used to study the overall configuration and dynamics of the magnetosphere and its interactions with the solar wind, Saturn's atmosphere, Titan, rings, and icy satellites.[7]

Radio Detection and Ranging Instrument (RADAR)

The Radio Detection and Ranging Instrument (RADAR) is a remote active and remote passive sensing instrument that will produce maps of Titan's surface and measures the height of surface objects (like mountains and canyons) by bouncing radio signals off of Titan's surface and timing their return. Radio waves can penetrate the thick veil of haze surrounding Titan. In addition to bouncing radio waves, the RADAR instrument will listen for radio waves that Saturn or its moons may be producing.[8]

Radio and Plasma Wave Science instrument (RPWS)

The Radio and Plasma Wave Science instrument (RPWS) is a direct and remote sensing instrument that receives and measures the radio signals coming from Saturn, including the radio waves given off by the interaction of the solar wind with Saturn and Titan. The major functions of the RPWS are to measure the electric and magnetic wave fields in the interplanetary medium and planetary magnetospheres. The instrument will also determine the electron density and temperature near Titan and in some regions of Saturn's magnetosphere. RPWS studies the configuration of Saturn's magnetic field and its relationship to Saturn Kilometric Radiation (SKR), as well as monitoring and mapping Saturn's ionosphere, plasma, and lightning from Saturn's (and possibly Titan's) atmosphere.[9]

Radio Science Subsystem (RSS)

The Radio Science Subsystem (RSS) is a remote sensing instrument that uses radio antennas on Earth to observe the way radio signals from the spacecraft change as they are sent through objects, such as Titan's atmosphere or Saturn's rings, or even behind the sun. The RSS also studies the compositions, pressures and temperatures of atmospheres and ionospheres, radial structure and particle size distribution within rings, body and system masses and gravitational waves. The instrument uses the spacecraft X-band communication link as well as S-band downlink and Ka-band uplink and downlink.[10]

Ultraviolet Imaging Spectrograph (UVIS)

The Ultraviolet Imaging Spectrograph (UVIS) is a remote sensing instrument that captures images of the ultraviolet light reflected off an object, such as the clouds of Saturn and/or its rings, to learn more about their structure and composition. Designed to measure ultraviolet light over wavelengths from 55.8 to 190 nm, this instrument is also a valuable tool to help determine the composition, distribution, aerosol particle content and temperatures of their atmospheres. This sensitive instrument is different from other types of spectrometers because it can take both spectral and spatial readings. It is particularly adept at determining the composition of gases. Spatial observations take a wide-by-narrow view, only one pixel tall and 60 pixels across. The spectral dimension is 1,024 pixels per spatial pixel. Additionally, it is capable of taking so many images that it can create movies to show the ways in which this material is moved around by other forces.[11]

Visible and Infrared Mapping Spectrometer (VIMS)

The Visible and Infrared Mapping Spectrometer (VIMS) is a remote sensing instrument that is actually made up of two cameras in one: one is used to measure visible wavelengths, the other infrared. VIMS captures images using visible and infrared light to learn more about the composition of moon surfaces, the rings, and the atmospheres of Saturn and Titan. VIMS also observes the sunlight and starlight that passes through the rings to learn more about ring structure. VIMS is designed to measure reflected and emitted radiation from atmospheres, rings and surfaces over wavelengths from 0.35 to 5.1 mm. It will also help determine the compositions, temperatures and structures of these objects. With VIMS, scientists also plan to perform long-term studies of cloud movement and morphology in the Saturn system, to determine the planet's weather patterns.[12]

I responded to this becuase I had been following both avenues Smolin spoke too, so I'll put my comment here as well.

This topic thread was develope from my reactions based on those who call people who are trying hard to integrate views of the natural world with the physics ideology of the topic of Strings?M theory, these fellows present. If they can not show us these new views as Smolin offers for inspection then what use the models and theories if no onne wants to se these work in the world we undrstand well by seeing around us?

While some people are looking for consistant means of determinations, others apply "conceptual situations" and bring forth comprehension of a kind. Now to this degree, that "gluonic perception is being adjusted" to see these values. The Smolins and others understood well the limitation of these views? Are there any?

Most of us understand the the aurora display do we not, and the resulting interactive play between the sun and the earth? The Auger experiment previously talked about and spoken too, by John Ellis, is a fine example of the diversity of interative features we can hope to see, as we examine the particle nature apart from the LHC rules of energy engagement, above and beyond the limits that have been imposed on us earthlings:)

While the topic is produced for this conversation seems disjointed, the ideology of the string theorist is held to a boundry of thinking in my eyes that such a membrane( here I could link a toy model for comparison), and defined in this bubble context, as rudimentry as it appears in my mind's eye, it follows the developemental processes we see from the eulicidation Einstein offered us by joining Maxwell into the process unfolding in nature and to see the effect of any bulk production as a necessary step beyond the boudaries of this bubble?

Now in contrast I see the soapy bubble and light refraction dispalyed in such a lovely continuous flow over it's surface, that to me, it does not make sense if such auroric dispalyes are not to give us new ideas about the interactive feature of the sun with earth? Conceptually, thes ideas of hitting metal plates and such present new ideas in how dispersion across that plate could represent other ideas. What are those. Wel that's what I am trying to do is free the mind from th econstraints we had put on it in sucha strick language accompany those that step ahead of us in their own specualtions educationally followed doctrine. What new light and thinking patterns follow these people?

Thursday, December 30, 2004

Once you see parts of the picture, belonging to the whole, then it becomes clear what a nice picture we will have?:) I used it originally for the question of the idea of a royal road to geometry, but have since progressed.

If you look dead center Plato reveals this one thing for us to consider, and to Aristotle, the question contained in the heading of this Blog.

It is beyond me sometimes to wonder how minds who are involved in the approaches of physics and mathematics might have never understood the world Gauss and Reimann revealled to us. The same imaging that moves such a mind for consideration, would have also seen how the dimensional values would have been very discriptive tool for understanding the dynamics at the quantum level?

As part of this process of comprehension for me, was trying to see this evolution of ordering of geometries and the topological integration we are lead too, in our apprehension of the dynamics of high energy considerations. If you follow Gr you understand the evolution too what became inclusive of the geometry developement, to know the physics must be further extended as a basis of our developing comprehension of the small and the large. It is such a easy deduction to understand that if you are facing energy problems in terms of what can be used in terms of our experimentation, that it must be moved to the cosmological pallette for determinations.

As much as we are lead to understand Gr and its cyclical rotation of Taylor and hulse, Mercuries orbits set our mind on how we shall perceive this quantum harmonic oscillator on such a grand scale,that such relevance between the quantum and cosmological world are really never to far apart?

As I have speculated in previous links and bringing to a fruitation, the methods of apprehension in euclidean determinations classically lead the mind into the further dynamcis brought into reality by saccheri was incorporated into Einsteins model of GR. Had Grossman not have shown Einstein of these geoemtrical tendencies would Einstein completed the comprehsive picture that we now see of what is signified as Gravity?

So lets assume then, that brane world is a very dynamcial understanding that hold many visual apparatus for consideration. For instance, how would three sphere might evolve from this?

Proper understanding of three sphere is essential in understanding how this would arise in what I understood of brane considerations.

INtegration of geometry with topological consideration then would have found this continuance in how we percieve the road leading to topolgical considerations of this sphere. Thus we would find the definition of sphere extended to higher in dimensions and value in brane world considerations as thus:

Sometimes it is very hard not to imagine this sphere would have these closed strings that would issue from its poles and expand to its circumference, as in some poincare projection of a radius value seen in 1r. It is troubling to me that the exchange from energy to matter considerations would have seen this topological expression turn itself inside/out only after collapsing, that pre definition of expression would have found the evoltuion to this sphere necessary.

Escher's imaging is very interesting here. The tree structure of these strings going along the length of the cylinder would vary in the structure of its cosmic string length based on this energy determination of the KK tower. The imaging of this closed string is very powerful when seen in the context of how it moves along the length of that cylinder. Along the cosmic string.

To get to this point:) and having shown a Platonic expression of simplices of the sphere, also integration of higher dimension values determined from a monte carlo effect determnation of quantum gravity. John Baez migh have been proud of such a model with such discrete functions?:) But how the heck would you determine the toplogical function of that sphere in higher dimensional vaues other then in nodal point flippings of energy concentration, revealled in that monte carlo model?

Topological consideration would need to be smooth, and without this structure how would you define such collpases in our universe, if you did not consider the blackhole?

So part of the developement here was to understand where I should go with the physics, to point out the evolving consideration in experimentation that would move our minds to consider how such supersymmetrical realities would have been realized in the models of the early universe understanding. How such views would have been revealled in our understanding within that cosmo?

One needed to be able to understand the scale feature of gravity from the very strong to the very weak in order to explain this developing concept of geometry and topological consideration no less then what Einstein did for us, we must do again in some comprehensive model of application.